Overview
This page is structured as follows:
In this section (Introduction) after a short welcome, overview, and the exhibition of some hopefully motivational pictures we will have a quick glimpse on how we usually plot (real) functions, then we will present the idea of the colorful visualization (domain coloring) in then case of complex functions.
Of course we can only understand this method well by examining its action on lots of examples and compare what we see with our former knowledge about complex functions. That is the aim of the second section entitled Functions: we plot lots of functions and recall their important properties.
Overview: the 'eyes' of a function.
In the third section (Series) we will present some function series (and sums) mainly because of them being interesting, but we shall arrive at some further conclusions. (E.g.: How does a complex Taylor sum converge? How can we approximate the Mandelbrot set?)
The title of the fourth section is pretty self-explanatory: (my) Favourites. Hopefully others will like these plots too…
In the section of Other methods we will mention—for the sake of completeness—some other (perhaps more traditional) possible ways of visualizing complex functions.
Under References we have collected a couple of links to web pages devoted to this topic—without the need for completeness. (Though I am aware of these now, I have developed my method and implemented my programs a while ago [in 2006] independently, without the knowledge of these; so to say reinventing what others already have found decades before me. And some surely will in the future…)
I have prepared quite a few presentations and essays regarding this topic and I still spread the word of this method unwaveringly, because it is just so beautiful and I think it is worth to get acquainted with. Perhaps it will be also useful in research activity. My collected works are available on this page.